Sentence examples for gives regularity from inspiring English sources

The paper gives regularity conditions under which the proposed two-step estimators are consistent and asymptotically normal; a Monte Carlo study compares the finite sample behavior of the proposed methods with their one-step counterparts.

In addition, when mesh is refined under a given regularity condition, a sufficiently smooth target function can be approximated by its interpolated function with arbitrary accuracy, meaning that the interpolation error norm approaches to zero.

The values of the average grain heights are correlated to the values of the average grain areas and are localized in a limited area, indicating a given regularity during the different carbon depositions.

We first give regularity conditions for model (1).

A curve was then fitted to these datapoints, and the hard disk diameter necessary to achieve a given regularity index was read off of this curve.

If Σ and μ do not represent the true model but the alternative model (Σ0 and μ0), and given regularity conditions are satisfied (practically amounting to multivariate normality, limited misfit and large sample size N), the test statistic T follows a non-central χ distribution with df0 degrees of freedom and non-centrality parameter λ, i.e., T ∼ χ(df0, λ), where λ > 0.

One set of results gives microlocal regularity of such a function away from the conormal bundle of a foliation.

The other set of results gives local regularity of solutions to a class of elliptic systems with fairly rough coefficients.

It is observed that the proposed filter bank gives more regularity and better frequency selectivity as compared to existing filter banks.

In [7], Fan gives the regularity of weak solutions for differential equations with variable exponent.

The discrepancy associated with the size of ZnS nanoparticles found from XRD and SEM may be because of the fact that SEM shows the lateral dimension of the particles whereas XRD gives the regularity in the atomic arrangement.